Question

Solve the equation:
$5x + 2\dfrac{3}{5} = 9 - \dfrac{4}{5}x$

Answer 1

Hint: Bring all the x terms on one side and known values on the other to solve for x. We can solve the fraction by taking LCM.
Complete step by step answer:
We have been given the following equation:
$ \Rightarrow 5x + 2\dfrac{3}{5} = 9 - \dfrac{4}{5}x$
Here the second term on the left hand side is a mixed fraction and we need to convert in an improper fraction for moving ahead with the calculation. The whole number in front of the fraction is the quotient for the denominator. Converting terms as discussed, we get,
$\begin{gathered}
   \Rightarrow 5x + \dfrac{{(5 \times 2 + 3)}}{5} = 9 - \dfrac{4}{5}x \\
   \Rightarrow 5x + \dfrac{{13}}{5} = 9 - \dfrac{4}{5}x \\
\end{gathered} $
Now we will bring $x$ terms on one side and known terms on the other. Here we will bring our variable to the left hand side for conventional sake. We get,
$\begin{gathered}
   \Rightarrow 5x + \dfrac{4}{5}x = 9 - \dfrac{{13}}{5} \\
   \Rightarrow \dfrac{{5 \times 5 + 4}}{5}x = \dfrac{{9 \times 5 - 13}}{5} \\
   \Rightarrow 29x = 32 \\
   \Rightarrow x = \dfrac{{32}}{{29}} \\
\end{gathered} $
Thus we have a solution which is an improper fraction as the numerator is greater than the denominator.
Note: Be careful with the signs of the terms while operating on them and change of signs while moving them on the other side to the equation.